Electrical Vibration associated with a thin Conductor. 99 



In his theoretical discussion of this subject Abraham * 

 considers the vibration about a perfect conductor in the form 

 of an elongated ellipsoid of revolution. When the minor 

 axis (2 b) becomes negligibly small in comparison with the 

 major axis (I), the wave-length in free sether of the disturb- 

 ance due to the fundamental vibration is equal to 21. In 

 a second approximation Abraham obtains the following 

 expression for this wave-length : — 



\ = 2Z(l + 5-6e 2 ) 



where 1/e = 4 log* (l/b) . 



In the table, under the heading "X calculated/' are given 

 the wave-lengths deduced from this equation, and under 

 u k calculated," the ratio of these wave-lengths to the lengths 

 of the oscillators. 



A consideration of the evidence shows that Abraham's 

 expression gives a result for the wave-length which agrees 

 with the measured value within the present limits of experi- 

 mental error. This was Ives' conclusion in 1910, and the 

 results now published add to his statement but the weight 

 attached to confirmation from independent work. The 

 physical accuracy of Abraham's deduction is now sufficiently 

 well established for linear oscillators of known dimensions to 

 be used as standards in connexion with the measurement of 

 short electric waves. 



These results completely support Lord Rayleigh's f view 

 of the value of the wave-length of the vibration on a thin 

 straight terminated rod, and at least imply the experimental 

 verification of his contention "that the difference between 

 the half wave-length of the gravest vibration and the 

 length (/) of the rod (of uniform section) tends to vanish 

 relatively when the section is reduced without limit." 



The experiments lend no support to Macdonald's calcu- 

 lation, which requires that the numbers in the table under 

 the heading- u k observed" should be 2*'5. It would appear, 

 then, that Sarasin and De la Rive's well-known experiments 

 which, hitherto, have only been quantitatively described in 

 terms of Macdonald's theory, still await their explanation. 



The University of Svdnev, 

 September 24th, 1915." 



* Abraham, loc. cit. 



